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# lec12 - Lecture 12 Lecture P112 Agenda for today Agenda...

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Unformatted text preview: Lecture 12 Lecture P112, Feb 15, 2008 Agenda for today Agenda Friction Kinetic Static Fluid resistance (Drag) What is friction? What Direction? magnitude? Friction Friction Opposes relative motion (sliding friction or kinetic Opposes friction) or the tendency for such motion to start (static friction) (static Friction results in a force opposite to the direction Friction of relative motion of Force is parallel to the surface and perpendicular Force to the normal force N Surface Friction... Friction is caused by the “microscopic” interactions Friction between the two surfaces (intermolecular bonds form and break): form The best we can do is make an approximate model The for this complicated situation for Model for surface friction Model The heavier something is, the greater the The observed force due to friction It also depends strongly on the material and It surface: Kinetic Friction surface: f k = mk N µ k: coefficient of kinetic friction. Units? coefficient Direction: parallel to the surface and opposite Direction: direction of motion. Sliding friction Sliding ma j K K K Nf on b F iK ff on b W W=mg N2: Nf on b=W (v>0) (v<0) Quick problem Quick Block is sliding down an incline plane at Block and angle α (with friction). What’s the acceleration of the box? acceleration α solution solution fSonB NSonB å å Fx = W sin a - mk N = ma (1) Fy = N - W cosa = 0 WEonB y N = mg cosa (2) α Insert (2) into (1) to solve for a: x mg sin a - mk ( mg cosa ) = ma a = g(sin a - mk cosa ) Static friction Static Static friction Static Friction also involved when the objects are Friction not moving with respect to each other. not Minimum force you have to apply to just Minimum get the box to move: fs=µ sN get µ s > mk Static friction: f s £ ms N Static N F fF Quick problem Quick How would you measure µ s? How Example solution Example For example increase the angle of a ramp For until the block just starts to slide. until Just before it slides: net force must be zero! fSonB å å × Fx = W sin a - msN = 0 Fy = N - W cosa = 0 WEonB α 2 : N = W cosa sin a 2.in .1 : ms = cos a ms = tan a summary summary Friction acts parallel to surface of contact Opposes relative sliding motion or tendency for Opposes such motion to start such Kinetic (sliding) friction force: fk µ k=coefficienct of kinetic friction = mk N f Static (sticking) force: µ s=coefficient of static friction For any pair of surfaces: s £ ms N µ s > mk F F K Graph of force due to friction versus applied force versus F A A N F fF Fluid Resistance (Drag) Fluid Fluid resistance Fluid Direction? Opposes relative motion of fluid Direction? and object. and Magnitude? Will depend on the velocity, Magnitude? shape of the body, properties of the fluid shape Observation: at low speed it is proportional Observation: to v, at high speed, it is proportional to v2 to Drag forces Drag Oppose motion of an object through fluid (liquid or Oppose gas) gas) fd v (rel. to fluid) 2 approximate force laws: 1. Linear drag (low speeds, viscous fluids) (low fd = b v 2. Quadratic drag (high speeds, low viscosity fluids (gases) (high f d = Dv 2 For fast things moving through air, use the For quadratic drag formula quadratic Airplanes, raindrops, cars at high speed.. Quadratic Drag force Quadratic f d = Dv 1 D = cd A r 2 2 “Drag coefficient” cd Object’s front cross-sectional area A Fluid’s density ρ Fluid’s Air Drag in Auto Design: Air D = (1/2) C ρ A v2 (1/2) C: C: Air Drag in Auto Design: Air D = (1/2) C ρ A v2 Air Drag in Auto Design: Air D = (1/2) C ρ A v2 Jeep Cherokee: CD = 0.51, MPG=21 Air Drag in Ski Jumping: Air D = (1/2) C ρ A v2 Air Drag in Luge: Air D = (1/2) C ρ A v2 Record luge speed: 85 mi/h Air Drag in Cycling: Air D = (1/2) C ρ A v2 Air Drag in Cycling: Air D = (1/2) C ρ A v2 World Speed Records: 200 m, flying start: 71.3 km/h (~45 mi/h) 1 hour: 55.3 km/h (~35 mi/h) Air Drag in Cycling: Air D = (1/2) C ρ A v2 How fast could you cycle if you could eliminate air drag? Bonneville Salt Flats, Utah: Bonneville Salt Flats, Utah: John Howard, USA, 1985: Fred Rompelberg, NL, 1995: (Rompelberg was 50 years old at the time.) 152 mi/h 152 167 mi/h Bird Formations During Migration: Bird By taking advantage of upward moving air proupward duced by their neighbors, migrating birds traveling duced in “Vees" can travel 1.7 × as far as individual birds. (~40% energy savings/mile). (~40% Fish Schools Fish By swimming in synchrony in the correct formation, swimming each fish can take advantage of moving water created by the fish in front to reduce drag. created Fish swimming in schools can swim 2 to 6 times as long as individual fish. Terminal speed Terminal Consider a skydiver falling in air At first her velocity will be zero- no air resistance, At initial acceleration is g initial As she speeds up, the resisting force increases as well, As until it becomes equal to the weight of the skydiver until W = fd mg = Dv 2 At that time the acceleration becomes zero She has reached “terminal speed” She “terminal mg vt = D Summary Summary Kinetic Friction: Opposes relative Motion f k = mk N f £ ms N 2 Static Friction: Opposes direction relative motion would start Air Drag Opposes relative motion Slow: s fd = b v Fast: f d = Dv Terminal Velocity vt = mg D ...
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